Can I still use HCS for hosting if I want to use my own domain name (e.g. www.my-student-organization.com)?

Yes! If you don't have an account, you can request one now at http://www.hcs.harvard.edu/account-request. Then see http://www.hcs.harvard.edu/tutorials/vhosts for information on setting this up. Once everything is configured, your site will magically appear at your domain name. Amazing!